the Higgs mechanism

Here is a paradox at the heart of the Standard Model: the beautiful gauge symmetry that governs the forces flatly forbids the force carriers of the weak interaction from having mass, yet the W and Z bosons are among the heaviest particles we know. The Higgs mechanism is the resolution. It says the vacuum of empty space is not truly empty but filled everywhere by a field, and the interactions of particles with that field are what we perceive as mass. Wade through the Higgs field and you acquire inertia; the more strongly you couple, the heavier you are.

The Higgs mechanism is the electroweak realization of spontaneous symmetry breaking. A scalar field is introduced whose potential energy is lowest not at zero but at a nonzero value, so the field settles everywhere into a constant nonzero vacuum expectation value, v about 246 GeV. This spontaneously breaks the electroweak SU(2) x U(1) symmetry down to the U(1) of electromagnetism. The would-be massless Goldstone bosons of that breaking are absorbed, 'eaten', by the W+, W- and Z, which thereby acquire mass while the photon remains massless. Fermions get mass through separate Yukawa couplings to the same field, each fermion's mass being proportional to its coupling times v. The single leftover ripple of the field is the Higgs boson, discovered at the LHC in 2012.

It is essential to be honest about what the Higgs does and does not explain. It gives mass to the W, Z and the fundamental fermions, and its couplings account for the strange spread of quark and lepton masses, but only by fixing each coupling by hand, so it reorganizes the mystery rather than solving it. And it explains almost none of the mass of ordinary matter: over 98 percent of the mass of a proton is QCD binding energy, not the Higgs-given masses of its quarks. The Higgs gives elementary particles their intrinsic mass; the mass of the world you can hold is mostly the energy of the strong field.